See image — GOC and Organic Chemistry Basics Chemistry Question

💡 Solution & Explanation

Concept: The stability (and hence longest half-life) of a carbocation depends on how effectively the positive charge is delocalized or stabilized by the attached groups. Step 1 - Identify each carbocation: (a) Tricyclopropylcarbocation: central C+ flanked by three cyclopropyl groups (b) Triphenylcarbocation (trityl cation): central C+ flanked by three phenyl groups (c) Tricyclohexylcarbocation: central C+ flanked by three cyclohexyl groups (only hyperconjugation/inductive) (d) tert-Butyl cation: central C+ flanked by three methyl groups (hyperconjugation/inductive only) Step 2 - Evaluate stabilization mechanisms: - Option (d): tert-butyl cation is stabilized only by hyperconjugation and inductive donation from three methyl groups. Modest stability. - Option (c): three cyclohexyl groups provide slightly more hyperconjugation than methyl groups, but no resonance delocalization. Moderate stability. - Option (b): trityl cation has extensive resonance delocalization across three phenyl rings; the positive charge is spread over many carbon atoms. Very high stability. - Option (a): cyclopropyl groups stabilize adjacent carbocations through a special interaction called 'cyclopropylcarbinyl' or 'bisected' orbital overlap. The bent Walsh orbitals of cyclopropane rings overlap directly with the empty p-orbital of the carbocation, providing extraordinarily effective electron donation — even more effective per group than a phenyl ring, because the cyclopropyl C-C bonding electrons are held in a geometry that maximizes overlap with the empty orbital. Three cyclopropyl groups acting together produce the highest degree of stabilization among the options given. Step 3 - Compare (a) vs (b): Although triphenylcarbocation (b) is very stable due to aromatic resonance, the tricyclopropylcarbocation (a) is actually MORE stable because each cyclopropyl group donates electron density more efficiently into the empty p-orbital than a phenyl ring does (the Walsh orbitals of cyclopropane are better donors than the pi system of benzene due to direct sigma-type overlap). Experimental and theoretical studies confirm that the tricyclopropylcarbocation has exceptional stability, surpassing even the trityl cation. Step 4 - Why other options fail: - (b) Trityl cation is very stable but not as stable as tricyclopropylcarbocation. - (c) No resonance; less stable than (a) or (b). - (d) Least stabilized; shortest half-life. Conclusion: The tricyclopropylcarbocation (a) has the greatest stability due to maximum cyclopropylcarbinyl orbital overlap from three cyclopropyl groups, giving it the longest half-life. Therefore, the correct answer is A.